Galois Theory

Group

A group is just a collection of objects (i.e., elements in a set) that obey a few rules when combined or composed by an operation. In order for a set to be considered a group under a certain operation, each element must have an inverse, the set must have an identity element, the set must be closed, and the set must be associative under the operation.

Polynomial

Symmetry

Symmetry, in a mathematical sense, is a transformation that leaves an object invariant. Symmetry is perhaps most familiar as an artistic or aesthetic concept. Designs are said to be symmetric if they exhibit specific kinds of balance, repetition, and/or harmony. In mathematics, symmetry is more akin to something like "constancy," that is, how something can be manipulated without changing its form.